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rukka - I have been summoned! (Also, unrelated, but your username is the same as one of the main characters in a book a friend of mine is writing. O.O) Anyway, back on topic now! I don't watch any Mecha anime, and honestly I'm a sucker for a good setting myself, so this should be fun! ^_^
My first recommendation is
The Devil is a Part Timer, I know it exists in tangible form, because it is sitting on my shelf and staring at me. It's hilarious. Premise: a demon king invades a magical world with an army and four generals. They were winning until a half-angel hero appeared, and eventually caused the king and his one remaining general to flee through a portal to a random world in order to escape her. And that's how the wound up in Tokyo. As humans. With limited supplies of magic, no money, and no way back. The demons adjust surprisingly well, with the king getting a part-time job at MgRonald's and the general basically becoming a house wife. Until one day the king ran into the hero on his way to work...
Fairy Tail is a good one too if you can get around the fan service (which often makes me want to scream at the TV "How the **** does Erza's armor even work?!?!) It's a long one though, so friendly warning on that. The story follows a guild of wizards. The setting's actually pretty interesting in my opinion, and there is a
lot of character development (this extends beyond the four main characters - pretty much every reoccurring character gets some development. And there are a lot of reoccurring characters...) There's a
lot of seriously strong female characters, they just...don't have much clothing. To be fair, one of the male characters spends a lot of his screen time wandering around in his underwear. Also, the villains have a tendency to redeem themselves, so you might wind up regretting wishing some of them dead. Which has happened to me. Multiple times...
I'm a fan of
Yu Yu Hakusho, but that one isn't very well known. Probably because it's pretty old. Since the series is an older one so the art might bother you though. Premise: a delinquent is killed in an accident trying to save a kid. Surprisingly, he is offered a chance to be resurrected, and manages it with help from his rival (another delinquent, who has psychic abilities,) and his best friend/longtime crush. After being resurrected he is appointed 'Spirit Detective' which doesn't really involve much detective work, mostly beating up demons. This quickly becomes a group activity. Good show overall, but in the English dub (don't know about the sub version) one of the character's keeps getting his age changed! It changes every time it's mentioned and that annoyed me a lot...
If you like mysteries
Case Closed is a good one, but the art style is
very unusual, and takes some getting used to. Also, the characters in the English dub version have different names than they do in the subbed version. Since I'm only familiar with the dub names, I'm not mentioning anyone's name in my description. Premise: the main character is a teenage detective who gets shrunk into a kid after confronting a pair of men. Following his transformation he winds up living with his best friend/crush in the hopes that her dad (who is a detective) might come across some information about the men, which he could use to find them and find a way to be cured. Unfortunately, her father is a very, very bad detective, so he mostly just gets used by the main character as a ventriloquist dummy so he can solve cases. Also, the friend/crush is terrifying, knows karate, and can and will dent metal by kicking it...
Monthly Girl's Nozaki-kun is really funny. Plus, the characters interact in very entertaining ways, and range of different personalities. Premise: the main character tried to tell a boy that she liked him, and somehow wound up being hired as his assistant instead! The guy in question is the creator of a popular romance manga and is constantly drawing on the things going on around him as material for it. For example, the assistant in charge of drawing flowers and special effects is the basis for the manga's female main character. A wide variety of plot ideas are tested out on his assistants (there's eventually four of them.) Plus, their school has a lot of really weird people attending it. Entertaining, but weird. So Nozaki is never starved for material!
That's all I'm going to recommend for now, but I'd be happy to give you more if you like! ^_^
(I actually know a lot more...)
-Edit - I can also add images to this if you like so you can see the art styles.